Jack superpolynomials, superpartition ordering and determinantal formulas

TL;DR

This paper introduces Jack superpolynomials as eigenfunctions of a supersymmetric model, establishing a superpartition ordering and deriving explicit determinantal formulas for these polynomials.

Contribution

It defines a new ordering on superpartitions and provides a simple determinantal expression for Jack superpolynomials, advancing understanding of supersymmetric integrable models.

Findings

Established superpartition ordering from Hamiltonian action

Defined Jack superpolynomials with triangular decomposition

Derived explicit determinantal formulas for Jack superpolynomials

Abstract

We call superpartitions the indices of the eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model. We obtain an ordering on superpartitions from the explicit action of the model's Hamiltonian on monomial superfunctions. This allows to define Jack superpolynomials as the unique eigenfunctions of the model that decompose triangularly, with respect to this ordering, on the basis of monomial superfunctions. This further leads to a simple and explicit determinantal expression for the Jack superpolynomials.